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The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and are allowed solutions of Schrodinger wave equation. Can you explain this statement

The existence of quantized electronic energy levels is a direct result of the wave like properties of electrons and are allowed solutions of Schrodinger wave equation.
 Can you explain this statement

Grade:11

1 Answers

Sunil Kumar FP
askIITians Faculty 183 Points
9 years ago
we have according to debroglie equation for wavelength of a particle
l=h/mv
where,l=wavelength of the particle
h=plancks constant
v=velocity of the electron
for electron, in a quantised state having particular energy level
radius of the energy level,2pir=n l
l=2pi*r/n
putting this value in eqn 1 ,we get
2*pi*r/n=h/mv
mvr=nh/2pi
Thus the existence of quantised energy level,(that is only those level where 2*pi*r=n*l is valid ),is a direct result of wave like property of electrons

The Schrödinger equation predicts that if certain properties of a system are measured, the result may be quantized, meaning that only specific discrete values can occur. One example is energy quantization: the energy of an electron in an atom is always one of the quantized energy levels, Another example is quantization of angular momentum. This was an assumption in the earlier Bohr model of the atom, but it is a prediction of the Schrödinger equation.

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